(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and...
(1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 + y2 = 9, and its height is 4. (a) Give a parametric equation, r(t) for the rim, C. r(t) with <t< (For this problem, enter your vector equation with angle-bracket notation: <f(t), g(t), h(t) >.) (b) If S is oriented outward and downward, find 's curl (-6yi + 6xj...
(1 pt) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 + y2 - 16, and its height is 2. (a) Give a parametric equation, r) for the rim, C. r(t) - (4cost,4sint,2) with O (b) If S is oriented outward and downward, find curl 7yi 7xj +3zk) d
(1 pt) The figure below open cylindrical can, S, standing on the...
Assignment 9: Problem 3 Previous Problem List Next (1 point) The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) The side of S is given by x2 +y2 = 9, and its height is 2. (a) Give a parametric equation, rt) for the rim, C r)= with (For this problem, enter your vector equation with angle-bracket notation: < f(t), g(t), h(t) >.) (b) If S is oriented outward and...
The figure below shows an open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but no top.) 2+49 (a) Give equation(s) for the rim, C. (Enter your answers as a comma-separated list of equations.) Cut-y7 + x7 + zk) . dA. (b) If S is oriented outward and downward, find curl(-yi + xj + zk) . dA =
The figure below shows an open cylindrical can, S, standing on the xy-plane. (S has a bottom...
The base of the closed cubelike surface shown here is the unit square in the xy-plane. The four sides lie in the planes x=0, x= 1, y = 0, and y= 1. The top is an arbitrary smooth surface whose identity is unknown. Let F= xi – 2yj + (z + 3)k and suppose the outward flux of F through Side A is 1 and through Side B is - 3. Can you conclude anything about the outward flux through...
(1 point) Let F(x, y, z) = 5yj and S be the closed vertical cylinder of height 4, with its base a circle of radius 3 on the xy-plane centered at the origin. S is oriented outward. (a) Compute the flux of F through S using the divergence theorem. Flux = Flux = || F . dà = (b) Compute the flux directly. Flux out of the top = Į! Įdollar Flux out of the bottom = Flux out of...
Help Entering Answers (1 point) Use Stokes' Theorem to evaluate ll curl F. dS where F(x, y, z) = xyzi + 3xyj + 2x2yzk and S consists of the top and the four sides (but not the bottom) of the cube with vertices (+2, +2, +2), oriented outward. Since the box is oriented outwards the boundary curve must be transversed when viewed from the top. A parametrization for the boundary curve C seen below from above can be given by:...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube 0 < x < 1, 0Sy, and 0szS 1 with open bottom in the ry plane. F(x, y, z)-<y, -, z > and the normal field n is oriented so that it points up on the top surface. T, zand
7. (16pts) Use Stokes, Theorem to find ▽ × F . nd.S where s is the surface of the cube...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
> parametrization order should be x=rsint, y=rcost
Gevorg Sat, Mar 26, 2022 4:30 PM